X-ray reflectometry (XRR) is a powerful technique to investigate surfaces and interfaces including their roughness, diffuseness across buried layers and thickness of single layer and multilayer stacks by depth profiling the electron density in the direction normal to the sample surface with a sub-nanometer resolution. It has also been shown that XRR is capable of quantifying the cross section profile of surface patterns, for example, in “Nano-imprint pattern transfer quality from specular x-ray reflectivity” by H. J. Lee et al. (APL, 2005), the cross section of line gratings fabricated by nano-imprint as well as the molds used to imprint the patterns have been measured via XRR. A similar application of XRR for measuring nanostructured surfaces has also been documented in U.S. Pat. No. 6,754,305. The efficacy and the limit of the application of XRR to nanoscale surface patterns are based on the effective medium approximation (EMA) as illustrated previously in “Determining Coherence Length of X-ray Beam Using Line Grating Structures” by H. J. Lee et al. (ECS Transactions, 2011). It should be noted that the equivalent concept of EMA has been used in estimating effective refractive index of porous material for ellipsometry or optical scatterometry as illustrated in “Annealing effect on the optical properties of implanted silicon in a silicon nitride matrix” by Z. H. Chen et al. (APL, 2008) and “Real-time studies of surface roughness development and reticulation mechanism of advanced photoresist materials during plasma processing” by A. R. Pal et al. (APL, 2009). The validity of EMA for nanostructures depends on the coherence length of the incident X-ray; only when the coherence length is greater than the lateral characteristic length of the nanostructure along the direction of interest EMA becomes applicable. In such cases, the structure space ratio at any given depth along the surface normal can be deduced from the XRR results. In summary, XRR can be used to measure film thickness as well as the cross sectional shape of nanostructures when the incidence X-ray possesses sufficient coherence length along the direction of interest.
In conventional XRR measurements, for examples, those described in U.S. Pat. No. 6,754,305, U.S. Pat. No. 7,039,158, and U.S. Pat. No. 6,711,232, a wavelength at 0.154 nm from a copper anode is often the preferred choice for measuring film structure; the typical angular range of measurements using X-ray of this wavelength is often between 0° to ˜4°. The footprint of X-ray will likely be in the millimeter range due to the low grazing incident angle involved, even for the cases that the incident X-ray is highly focused on the sample. The known focusing techniques such as described in U.S. Pat. No. 6,711,232 and DE 4,137,673 include the use of focusing mirror, curved monochromator and a combination of both. To further limit the size of the incident beam footprint on samples a blocking barrier has been proposed in U.S. Pat. No. 6,711,232. However, by placing a block barrier in the proximity of the sample surface can reduce the total incident beam flux and also inevitably introduce parasitic scatterings from the barrier edge. Both of the abovementioned side effects will serve to deteriorate the signal-to-noise ratio (SNR) of the measured reflection intensities. The characteristic reflection peaks from sample with a thickness of few nanometers are located at high q region where the reflectivity is intrinsically low, typically in 10−5 or below. In order to acquire signal at high q region with a sufficient SNR the measurement time can be prohibitively long for many applications given that the background noise of the detector is much lower than the weak signal. This low reflectivity or long data acquisition time coupled with a miniscule sample area will render the XRR measurement very challenging. The purpose of this invention is to address the abovementioned challenges and concurrently maintain a reasonable level of SNR as well as certain intricate features of the reflectivity and the q resolution in terms of δq/q.